Tag: thermal properties

Quizzes (8) Questions (112)

Questions Related to thermal properties

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of :

  1. 2

  2. 4

  3. 8

  4. 16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We know that from Stefan's Boltzmann relation: $E\propto { T }^{ 4 }$
if the temperature of the sun will be doubled, then : $E\propto ({ 2T })^{ 4 }$
Hence, $E\  will\  increase \ by \ the \ factor \ of \  { 16}$.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A black body is at temperature $300K$. It emits energy at a rate, which is proportional to 

  1. ${(300)}^{4}$

  2. ${(300)}^{3}$

  3. ${(300)}^{2}$

  4. $300$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For black body radiation
$E=\sigma{T}^{4}$ or $E\propto {T}^{4}$
Rate of emission of energy $\propto {(300)}^{4}$

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

If the absolute temperature of a blackbody is doubled, then the maximum energy density

  1. Increases to 16 times

  2. Increases to 32 times

  3. <span>Decreases</span>&nbsp;to 16 times

  4. Decreases to 32 times
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The power with which a body(in this case black body) radiates is directly proportional to the fourth power of absolute temperature:
$P = kT^{4}$
i.e.
$P _{1} = kT _{1}^{4}$
If the absolute temperature is doubled,
$P _{2} = k(2T _{1})^{4} = 16kT _{1}^{4}$
Now $\dfrac{P _{2}}{P _{1}} = \dfrac{16}{1}$ 

Hence energy density is increased 16 times.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Intensity of heat radiation emitted by body is believed to be proportional to fourth power of absolute temperature of the body. The proportionality constant also known as Boltzmann's constant may have possible value of :

  1. $5.67\times 10^{-8} watt/K^4 $

  2. $5.67\times 10^{-8} watt/m^2 K^4 $

  3. $5.67\times 10^{-8} J/K^4 $

  4. $5.67\times 10^{-8} Js/K^4 $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From the given question,

$I\propto T^4$

$I=k T^4$

where $k=$ Stefan-Boltzmann's constant

$k=5.67\times10^{-8} W/m^2K^4 $

The correct option is B.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A black body at a temperature of $227^oC$ radiates heat energy at the rate 5 cal/cm$^{2}-s$. At a temperature of $727^oC$, the rate of heat radiated per unit area in cal/cm$^2$ will be

  1. 80

  2. 160

  3. 250

  4. 500
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Stefen's Law, the rate of heat radiation from body is proportional to the fourth power of body's temperature.

Thus $P\propto T^4$
$\implies \dfrac{P _2}{P _1}=\dfrac{T _2^4}{T _1^4}$
$=16$
$\implies P _2=80cal/cm^2-s$

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

For a block body temperature $727^{o}C,$ its rate of energy loss is $20\ watt$ and temperature of surrounding is $227^{o}C.$ If temperature of black body is changed to $1227^{o}C$ then its rate of energy loss will be:

  1. $320\ W$

  2. $\dfrac {304}{3}\ W$

  3. $240 W$

  4. $120 W$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It is given that,

Temperature of surrounding

  $ {{T} _{0}}={{227}^{0}}C=500\ K $

 $ {{T} _{1}}={{727}^{0}}C=1000\ K $

 $ {{T} _{2}}={{1227}^{0}}C=1500\ K $

 $ {{E} _{1}}=20\ Watt\,\, $

 $ {{E} _{2}}=? $

According to Stefn boltzmann law:

$ E=\sigma {{T}^{4}} $

Or

 $ {{E} _{1}}=\sigma ({{T} _{1}}-{{T} _{0}})^4 $

 $ {{E} _{2}}=\sigma ({{T} _{2}}-{{T} _{0}})^4 $

Taking ratios of above equations:

For $ {{E} _{1}}=20\ Watt $

 $ \dfrac{20}{{{E} _{2}}}={{\left( \dfrac{500}{1000} \right)}^{4}} $

 $ \dfrac{20}{{{E} _{2}}}=\left( \dfrac{1}{16} \right) $

 $ {{E} _{2}}=320\ Watt $

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The power received at distance $d$ from a small metallic sphere of radius $r(<<d)$ and at absolute temperature $T$ is $P$. If the temperature is doubled and distance reduced to half of the initial value, then the power received at that point will be:

  1. $4p$

  2. $8p$

  3. $32p$

  4. $64p$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Energy received per second i.e., power $P\alpha \dfrac{T^4}{d^2}=k\dfrac{T^4}{d^2}$
if temperature is double than T become 2T and distance become half than d become $\dfrac{d}{2}$
than power $ p _{1}=k\dfrac{(2T)^4}{(\dfrac{d}{2})^2}=64k\dfrac{T^4}{d^2}=64P$
Hence D option is correct.
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

What is the value of solar constant if the energy received by $ 12$ m$^2$ area in $2$ minutes is $2016$ kJ?

  1. $1.4 \times 10^2 J s^{-1}&nbsp; m^{-2}$

  2. $1400 J s^{-1}m^{-2}$

  3. $84 kJ s^{-1} m^{-2}$

  4. $84 J s^{-1} m^{-2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Solar constant = Energy received by unit area in unit time from Sun
$=\cfrac{2016\times 10^3}{12\times (2\times 60)} \\=1400Js^{-1}m^2$
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

If a graph is plotted by taking spectral emissive power along $y-$axis and wavelength along x-axis is:

  1. Emissivity

  2. Total intensity of radiation

  3. Diffusivity

  4. Solar constant
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Emissive power varies according to Stefan-Boltzmann law as :

$E=\sigma {{T}^{4}}$

According to Planck’s distribution law:

${{E} _{\lambda }}(\lambda ,T)=\dfrac{{{C} _{1}}}{{{\lambda }^{5}}\left[ \exp (\dfrac{{{C} _{2}}}{\lambda T})-1 \right]}$

The graph shows that the emitted radiation varies with wavelength and also it shows Emissivity.

 

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A spherical body of area A and emissivity $0.6$ is kept inside a perfectly black body. Total heat radiated by the body at temperature T is?

  1. $0.4\sigma AT^4$

  2. $0.8\sigma AT^4$

  3. $0.6\sigma AT^4$

  4. $1.0\sigma AT^4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When a non black body is placed inside a hollow enclosure the total radiation from the body is the sum of what it would emit in the open ( with e<1 ) and the part (1-a) of the incident radiation from the walls reflected by it.

The two add up to a black body radiation . Hence the total radiation emitted by the body is $1.0\sigma AT^4$
1.0σAT4.